How to make a rope in the BGE?
The are two main ways to make a rope in the BGE. Soft bodies, and ridged body constraints. 

The ridged body constraint method.
This is the method Phymec uses in videos like this. I have not gotten good results with soft bodies, so I will focus on the ridged body constraint method.
This is very easy to set up, just add a sphere, model it in to a capsule and add a Rigid Body Joint constraint.

Then string many of the capsules in to a rope, with the next always having the target of the one before it. Set the Pivot to be in the middle of the two capsules (turn on Display Pivot to see where the pivot point is).  Also important turn on Linked Collision; if not on the rope will try to break apart where ever it is intersecting.